5. Computation of Failure Probabilities
The test results for Atlas, Delta, and Titan in the tables of Appendix D have been used
for three primary purposes:
  (1) To predict or estimate the overall probability that each vehicle will fail during the
      various phases of flight (see Table 39, Appendix D, for flight-phase definitions).

  (2) To establish the relative and overall probabilities for Response Modes 1 through 5..
  (3) To establish the relative frequency of tumble for Response Modes 3 and 4.

5.1 Overall Failure Probat>ility

To- predict failure probabilities for Atlas, Delta, and Titan, the test results in
Appendix D for representative configurations (i.e., "l" in last column) have been
filtered using three different weighting techniques described in Appendix C:
  (1) Equal weighting
  (2) Index-count .weighting
  (3) Exponential weighting
 In computing filtered or weighted failure probabilities, a test is assigned a score of one
 to indicate the occurrence of a failure or some anomalous behavior, and a score of zero
 if no failure occurred. Admittedly, there may be disagreements about the classification
 of a few flights, since the launch agency may consider as successful or partially
 successful some flights that are shown as failures in· Appendix D. To avoid such
 disagreements, it is better to- think of some non-normal events, particularly those
 occurring late in flight, as anomalies rather than failures. The flight phases, as shown
 in column 2 of Table 2 and defined in Appendix D.1.3, are inclusive; e.g., flight phase
 "0 - 3" includes phases 0, 1, 1.5, 2, 2.5, and 3. An 'NA' in the response-mode column in
 the tables of Appendix D indicates that some failure or anomalous behavior has had an
.effect on the final orbit or impact point without producing additional risks to people on
 the ground or necessarily failing the mission. In the failure-probability calculations of
 Table 2 and Table 3, an 'NA' has been- considered as a success for all flight phases
 except "0 - 5", irrespective of the phase in which the failure or anomalous behavior took
 place. Only in flight phase "0- 5" is an 'NA' response considered a failure. The
 filtered results for representative configurations (defined in Appendix D.1.4) are given
 in Table 2 for six flight phases. For flights with multiple entries in the Response-Mode
 and Flight-Phase columns (e.g., see Appendix D.2.1, No. 257), the first listed value was
 used in the filtering process.




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